Abstract
The main purpose of this paper is using the analytic method and the orthogonal properties of the character sums to study the computational problem of one kind hybrid power mean of the generalized Gauss sums operatorname{mod} p, an odd prime with pequiv 1operatorname{mod} 3, and give some exact computational formulas for this kind hybrid power mean.
Highlights
Let q ≥ be a positive integer, χ be any Dirichlet character mod q
Hereinafter, we shall use many elementary number theory knowledge and the properties of the classical Gauss sums and Dirichlet characters, all of them can be found in reference [ ], so we do not repeat them here
Note that if p ≡ mod , τ (χ ) = –p and A(p) is a pure imaginary number, so from ( ) and the definition of A(p) we may immediately deduce Theorem
Summary
1 Introduction Let q ≥ be a positive integer, χ be any Dirichlet character mod q. Zhang Wenpeng and Liu Huaning [ ] studied the fourth power mean of the generalized third Gauss sums with |(p – ), and they obtained a complex but exact computational formula. We are concerned with the computational problem of the following hybrid power mean: p– p–
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